1. Field of the Invention
The present invention relates generally to digital image processing, and more particularly, to a technique for measuring a two-dimensional point spread function (PSF) of a digital image acquisition system.
2. Description of Related Art
An important characteristic of a digital image acquisition system, such as a digital camera, is its ability to resolve the detail of an original scene in a recorded image. Factors that affect the resolution at which a digital image acquisition system can record an original scene include the quality of the system's optics, the resolution or response of the system's CCD sensor array, and the effectiveness of the system's integrated image processing components directed at correcting image defects. There exists a number of different resolution metrics for measuring the ability of a digital image acquisition system to preserve the sharpness of an original scene in a recorded image.
One resolution metric that measures the amount of blur introduced into a recorded image is known as a camera's point spread function (PSF). By definition, the PSF of a camera provides a metric for determining the degree to which a perfect point in an original scene is blurred in a recorded image. In other words, the PSF is the image of a point source. More specifically, the PSF is the two-dimensional impulse response of a digital image acquisition system. Generally, digital image acquisition systems gradually lose the ability to contrast detail as the detail in an original scene becomes finer and finer. Thus, digital image acquisition systems tend to have a PSF that is significantly larger than an ideal dot because of the system's finite optical aperture and the spacing, shape and size of the optical sensor array elements. Many digital image acquisition systems are well approximated by linear systems. Consequently, blurred images recorded by them can be considered the superposition of the PSF of all points in the imaged object. As such, blurring is essentially the convolution of an image with a PSF.
The spatial frequency response of a digital image acquisition system is the two-dimensional Fourier transform of the PSF, which is defined as the optical transfer function (OTF). The modulus of the OTF is the modulation transfer function (MTF). In other words, the MTF is the magnitude of the OTF. The MTF provides a continuous measure of the contrast response of a digital image acquisition system to a range of spatial frequencies. If a digital image acquisition system were able to record an image that is an exact replica of an original scene, the contrast of the recorded image would be exactly the same as the contrast of the original scene at all frequencies. In reality, however, digital image acquisition systems are unable to maintain the contrast at higher frequencies, thereby recording a blurred image of an original scene.
The recorded blurred image of an original scene can be corrected with a restoration filter, which can be designed using knowledge of a PSF. The restoration filter sharpens recorded images of an original scene by removing the blurring introduced by the digital image acquisition system. By way of example, a very simple restoration filter that removes image blur, and thereby sharpens a recorded image, is an inverse filter that divides the two-dimensional Fourier transform of the recorded image by the optical transfer function of the digital image acquisition system. In effect, accurately measuring the PSF for a digital image acquisition system provides both a metric for defining the system's ability to preserve detail as well as a transfer function for correcting the blurring introduced by imperfect optical components of the system.
There exist two basic classes of methods for estimating a digital image acquisition system's PSF: calibration methods and blind methods. Generally, calibration methods require the user of a camera scanning system to acquire an image of a special page, whereas blind methods can be used with no user intervention. More specifically, calibration methods require that an image of a known scene (i.e., a test chart) be recorded. The special properties of the known scene enable more accurate estimation of the PSF. In contrast, blind methods make very simple assumptions about the blur and an original scene. Although blind methods enable the estimation of a PSF from arbitrary images, blind methods generally tend to produce less accurate results and run slower than calibration methods.
Two commonly used calibration methods for estimating a PSF are the knife-edge method and the random noise pattern methods. The knife-edge method is disclosed by Reichenbach et al., in "Characterizing Digital Image Acquisition Devices," Optical Engineering Vol. 30, No. 2., pp. 170-177, Feb. 1991 (also disclosed in ISO Standard 12233--"Photography--Electronic Still Picture Cameras--Resolution Measurements," 1997). Generally, the knife-edge method estimates a PSF from a recorded image of a slanted straight-edged discontinuity in image intensity. The distance from the edge is used to super-resolve the image to estimate the super-resolved edge-spread function. Under the assumption of circular symmetry, the derivative of the edge-spread function provides an estimate of the PSF.
The random noise method, which is disclosed by Hong et al., in "Measuring The MTF For Focal-Plane Arrays Using Random Noise Targets," Measurement Science and Technology Vol. 7, No. 7, pp.1087-1091, 1996, uses an image of white noise (i.e., noise with equal power at each spatial frequency) to measure MTF. The noise is usually printed as a random black and white dot pattern in order to maximize signal-to-noise ratio and for ease of printing. The random noise method relies on the observation that the power spectrum of blurred white noise is the same as the power spectrum of the blur, in the absence of further additive noise. This method may be used to estimate the aliased point spread function in two-dimensions. Another alternative is to super-resolve a one-dimensional estimate of the PSF by expanding a one-dimensional white noise test pattern into a series of lines. If the lines are slanted, the same super-resolution technique as used in the knife-edge method may be applied.
Neither the knife-edge method nor the random noise methods are very accurate measures of the two-dimensional PSF. The knife-edge method estimates the two-dimensional PSF by assuming that a one-dimensional point spread function is symmetric. However, it is not always accurate to assume that a PSF is symmetric for some of the following reasons. First, camera optics may give rise to asymmetric effects such as coma. Second, CCD or CMOS elements in digital cameras tend not to have symmetric optical sensitivities. In addition, although the random noise method estimates a two-dimensional PSF, it is a limited estimate of a two-dimensional PSF because it only estimates the magnitude of the PSF, and not its sign or phase.
Accordingly, it would be advantageous to provide an improved method for measuring a two-dimensional PSF. Furthermore, it would be advantageous if the improved method for measuring a two-dimensional PSF did not assume that image acquisition systems have a PSF with symmetric properties. One motivation for developing a more accurate method for measuring a digital image acquisition system's PSF is that digital cameras are increasingly used as an interface to display and record images of documents. Unlike document scanning devices such as a flatbed, a hand-held, or a sheet-fed scanner, digital cameras operate under less controlled conditions. That is, the images recorded with digital cameras have lower resolutions and therefore tend to be blurrier than images recorded with document scanners. Blur introduced into recorded images by imperfect electro-optical recording systems can be corrected by accurately estimating the PSF of the recording systems.